Solve sqrt{3}X-x-4/tan36^circ=16.4

$$\sqrt { 3 } X - \frac { x - 4 } { \tan 36 ^ { \circ } } = 16.4$$

Solve for X

$$X=\frac{2\sqrt{3}\left(3125000000000000x+24735304560274741\right)}{13622672400100515}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\sqrt{3} X - \frac{x - 4}{0.7265425280053608} = 16.4$$

Divide each term of x-4 by 0.7265425280053608 to get \frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}\right)=16.4$$

Expand \frac{-4}{0.7265425280053608} by multiplying both numerator and the denominator by 10000000000000000.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-40000000000000000}{7265425280053608}\right)=16.4$$

Reduce the fraction \frac{-40000000000000000}{7265425280053608} to lowest terms by extracting and canceling out 8.

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}\right)=16.4$$

To find the opposite of \frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}, find the opposite of each term.

$$\sqrt{3}X-\frac{x}{0.7265425280053608}+\frac{5000000000000000}{908178160006701}=16.4$$

Add \frac{x}{0.7265425280053608} to both sides.

$$\sqrt{3}X+\frac{5000000000000000}{908178160006701}=16.4+\frac{x}{0.7265425280053608}$$

Subtract \frac{5000000000000000}{908178160006701} from both sides.

$$\sqrt{3}X=16.4+\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}$$

Subtract \frac{5000000000000000}{908178160006701} from 16.4 to get \frac{49470609120549482}{4540890800033505}.

$$\sqrt{3}X=\frac{49470609120549482}{4540890800033505}+\frac{x}{0.7265425280053608}$$

The equation is in standard form.

$$\sqrt{3}X=\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}X}{\sqrt{3}}=\frac{\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}}{\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$X=\frac{\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}}{\sqrt{3}}$$

Divide \frac{49470609120549482}{4540890800033505}+\frac{1250000000000000x}{908178160006701} by \sqrt{3}.

$$X=\frac{2\sqrt{3}\left(3125000000000000x+24735304560274741\right)}{13622672400100515}$$

Solve for x

$$x=\frac{908178160006701\sqrt{3}X}{1250000000000000}-7.91529745928791712$$